Financial/Actuarial Mathematics Seminar

Van Eenam Lecture #3: The Harrison-Shepp Equation and some of Its Offspring

In a pioneering article from 1981, Harrison and Shepp provided a stochastic integral equation characterizing the skew Brownian motion of Ito & McKean (1963). We provide similar characterizations for skew-reflected scalar semimartingales, and for a class of planar processes with a roundhouse singularity at the origin which we call "Walsh semimartingales" and which include the Walsh Brownian motion as a special case. Armed with this description, and with an associated stochastic calculus that we develop, we formulate and solve problems of optimal control with discretionary stopping for such Walsh semimartingales. (Joint work with Tomoyuki Ichiba, Vilmos Prokaj and Minghan Yan.)
Speaker(s): Ioannis Karatzas (Columbia University)